Line a 8"x8"x2" square pan with aluminum foil. Butter the pan with 1 tablespoon of the butter. Butter the bottom and sides of a 2-quart heavy saucepan with 1 teaspoon of the butter.

Combine the sugars, cream, chocolate, and corn syrup in the saucepan. Place over medium heat and cook until the mixture reaches a boil, stirring constantly. Carefully clip a candy thermometer to the side of the pan. Continue to cook, stirring constantly, until the mixture reaches the soft ball stage, (234°F), about 20 minutes.

Remove from the heat and add the remaining butter and vanilla. Let the mixture stand, without stirring, for about 1 hour or until the mixture reaches 110°F.

Remove the candy thermometer. Using a wooden spoon, beat the mixture continuously until the mixture thickens. Add the nuts and continue to beat the mixture for about 10 minutes, or until very thick and loses shine.

Spread the mixture in the prepared pan. Using a knife, score the mixture into individual squares. Let the mixture set completely. Carefully lift the foil from the pan and cut the fudge into individual squares.